This article is devoted to study of vector functions in Banach algebras and Banach spaces over normed fields. A structure of their Banach algebras is investigated. Banach algebras of vector functions with values in ∗-algebras, finely regular algebras, B∗-algebras, and operator algebras are scrutinized. An approximation of vector functions is investigated. The realizations of these algebras by operator algebras are studied.
